Animate Collision On and Off
The answer is: No

You can not directly animate the modifier so that it will be cloth-permeable, but you can easily find ways around it.

I fixed this problem by running a simple small animation myself, a cloth plane falling on a cube with collision settings, and a large plane (with collision settings to act as the floor).

I animated the cube with a LocScale keyframe at frame 1, 50, and 75.

At frame one I added a single keyframe to the cube without doing anything.

At frame 50, I did nothing to the cube, and set another keyframe.

At frame 75, I scaled the cube down to .0001 size, and moved it beneath the plane.

The final result is that the cube shrinks below the cloth, and gives the effect of the object disappearing. 

I believe this is the best way to animate these kinds of simulations, so I hope this helps you.

Here is the .blend. (Note: you may need to re-bake the cloth):


Here is a video, too, if you don't want to have to download the .blend.